If you changed the angles, you wouldn't have the same kind of shape anymore. For example, in a square, all of the angles are 90°. If you double them all, you will simply have a straight line (a bunch of 180° angles lined up), which is certainly not "similar" to a square. If we start with a triangle, the angle sum is 180°. If we double all of the angles, we would end up with something with angles summed to 360&deg -- certainly not a triangle, and not similar to what we started with.

The new coordinates are (2b1,2b2) and (2a1,2a2). The new distance is . The new distance is double the original distance. We can show this by factoring the 22 from the second expression, obtaining the following:

We would need to find at least two well-defined reference points on the figure (such as the two endpoints of the spirals). In relation to these two points and the line they define, we could establish pairs of corresponding points on the two shapes. We would then require that all of the distances between all pairs of corresponding points be proportional.